Soak 18 wooden skewers in water 20 minutes. Thread the watermelon, pineapple and mango cubes on the skewers. Put the skewers in a large zip-top plastic bag, being careful not to puncture the bag; add the lime juice, seal and toss gently to incorporate. Refrigerate at least 30 minutes or until ready to use.
Preheat a grill or grill pan to medium high. Remove the skewers from the bag and place on a baking sheet. Brush the fruit with vegetable oil and place the skewers on the grill. Grill, turning once, until marks appear, 6 to 8 minutes. Transfer to a serving platter.
Combine the lime zest, chili powder and 1 teaspoon salt in a small bowl. Sprinkle the seasoning over the grilled fruit.